I have seen two characterizations of the problem in measuring a discrete variable of a state ψ exactly with each of two non-commuting Hermitian operators A and B:(adsbygoogle = window.adsbygoogle || []).push({});

(1) that the product of the standard deviations ( = √(<ψ|A^{2}|ψ>-<ψ|A|ψ>^{2}), & ditto for B) ≥ 1

(2) that one cannot simultaneously diagonalize the matrix representations of A and B

(i.e., if A = U^{†}CU and B = V^{†}DV, for unitary U and V and diagonal C and D, with^{†}denoting the adjoint, then U≠V.

Where is the link between these two?

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# Diagonalizabilty versus spread for uncertainty (discrete)

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